Most Popular
1500 questions
80
votes
0 answers
Is there a "ping-pong lemma proof" that $\langle x \mapsto x+1,x \mapsto x^3 \rangle$ is a free group of rank 2?
Let $f,g\colon \mathbb R \to \mathbb R$ be the permutations defined by $f\colon x \mapsto x+1$ and $g\colon x \mapsto x^3$, or maybe even have $g\colon x \mapsto x^p$, $p$ an odd prime.
In the book, by Pierre de la Harpe, Topics in Geometric Group…
user29123
80
votes
4 answers
Is the product of symmetric positive semidefinite matrices positive definite?
I see on Wikipedia that the product of two commuting symmetric positive definite matrices is also positive definite. Does the same result hold for the product of two positive semidefinite matrices?
My proof of the positive definite case falls apart…
nullUser
- 28,703
80
votes
10 answers
Is there a shape with infinite area but finite perimeter?
Is this really possible? Is there any other example of this other than the Koch Snowflake? If so can you prove that example to be true?
Chris Truong
- 801
79
votes
2 answers
What are the formal names of operands and results for basic operations?
I'm trying to mentally summarize the names of the operands for basic operations. I've got this so far:
Addition: Augend + Addend = Sum.
Subtraction: Minuend - Subtrahend = Difference.
Multiplication: Multiplicand × Multiplier = Product. Generally,…
trw
- 1,073
- 1
- 8
- 15
79
votes
7 answers
What is the main difference between a vector space and a field?
In my opinion both are almost same. However there should be some differenes like any two elements can be multiplied in a field but it is not allowed in vector space as only scalar multiplication is allowed where scalars are from the field.
Could…
Vineel Kumar Veludandi
- 1,075
79
votes
5 answers
Difference between axioms, theorems, postulates, corollaries, and hypotheses
I've heard all these terms thrown about in proofs and in geometry, but what are the differences and relationships between them? Examples would be awesome! :)
Gordon Gustafson
- 3,475
79
votes
4 answers
Limit $\frac{x^2y}{x^4+y^2}$ is found using polar coordinates but it is not supposed to exist.
Consider the following 2-variable function:
$$f(x,y) = \frac{x^2y}{x^4+y^2}$$
I would like to find the limit of this function as $(x,y) \rightarrow (0,0)$.
I used polar coordinates instead of solving explicitly in $\mathbb R^2 $, and it went as…
mesllo
- 1,490
79
votes
14 answers
Good books on mathematical logic?
I just started to learn mathematical logic. I'm a graduate student. I need a book with relatively more examples. Any recommendation?
ciciplus
79
votes
9 answers
What is the math behind the game Spot It?
I just purchased the game Spot It. As per this site, the structure of the game is as follows:
Game has 55 round playing cards. Each card has eight randomly placed symbols. There are a total of 50 different symbols through the deck. The most…
Javid Jamae
- 894
79
votes
13 answers
Why are addition and multiplication commutative, but not exponentiation?
We know that the addition and multiplication operators are both commutative, and the exponentiation operator is not. My question is why.
As background there are plenty of mathematical schemes that can be used to define these operators. One of these…
rob levin
- 791
79
votes
10 answers
Examples of finite nonabelian groups.
Can anybody provide some examples of finite nonabelian groups which are not symmetric groups or dihedral groups?
kalpeshmpopat
- 3,362
79
votes
9 answers
What do $\pi$ and $e$ stand for in the normal distribution formula?
I'm a beginner in mathematics and there is one thing that I've been wondering about recently. The formula for the normal distribution is:
$$f(x)=\frac{1}{\sqrt{2\pi\sigma^2}}e^{-\displaystyle{\frac{(x-\mu)^2}{2\sigma^2}}},$$
However, what are $e$…
pimvdb
- 1,293
79
votes
7 answers
Bag of tricks in Advanced Calculus/ Real Analysis/Complex Analysis
I am studying for an exam and I have been studying my butt off
during the winter break for it. During the course of my study I have written
down quite a number of tricks, which in my opinion were 'outrageous' :-). Meaning there
was no way I would…
Cousin
- 3,625
79
votes
9 answers
Probability of 3 people in a room of 30 having the same birthday
I have been looking at the birthday problem (http://en.wikipedia.org/wiki/Birthday_problem) and I am trying to figure out what the probability of 3 people sharing a birthday in a room of 30 people is. (Instead of 2).
I thought I understood the…
irl_irl
- 893
79
votes
5 answers
Drunk man with a set of keys.
I found this problem in a contest of years ago, but I'm not very good at probability, so I prefer to see how you do it:
A man gets drunk half of the days of a month. To open his house, he has a set of keys with $5$ keys that are all very similar,…
iam_agf
- 5,518